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Proof step 2 from proof sub-same (previous step)

n ≤ m ⊦ m - (m - n) = n

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: nat inst: name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [m, m - n, n0] flags: rewrite, current

Additional information

Used simplifier rules: lels-01: ⊦ ¬ m ≤ n ↔ n < m;%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false);%ls-03: n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0;%lels-01: ⊦ ¬ m ≤ n ↔ n < m;%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false);%eq-02: n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1;%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%l-02: ⊦ ¬ m + n < m; from specification nat-basic2 Used terms: m, m - n, n0